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SUMMARY:Group generators and relations\, and making balls of triangles - R
 ichard Parker
DTSTART:20090202T160000Z
DTEND:20090202T170000Z
UID:TALK16431@talks.cam.ac.uk
CONTACT:Anton Evseev
DESCRIPTION:Generators and relations for a group can always be put into th
 e form where all relations are of length three.  Any word that is the iden
 tity in the group must then be the boundary of a region filled in with tri
 angles.\nIt is therefore critical to understand what a region can look lik
 e that has a lot of triangles and a short boundary. Of course in that case
  the remainder\nof the sphere can be filled in with a few more triangles\,
  so the real question is to understand something about balls made of trian
 gles.\n\nFor example\, one can define the curvature of a vertex to be 6 - 
 &#60\;number of triangles meeting at that vertex&#62\;.  Can one then make
  the ball one vertex at a time\, remaining connected and having positive t
 otal curvature?\n\nI feel there is a whole new subject here!
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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